Variational learning for inverse problems

Tonolini, Francesco (2021) Variational learning for inverse problems. PhD thesis, University of Glasgow.

Abstract

Machine learning methods for solving inverse problems require uncertainty estimation to be reliable in real settings. While deep variational models offer a computationally tractable way of recovering complex uncertainties, they need large supervised data volumes to be trained, which in many practical applications requires prohibitively expensive collections with specific instruments. This thesis introduces two novel frameworks to train variational inference models for inverse problems, in semi-supervised and unsupervised settings respectively. In the former, a realistic scenario is considered, where few experimentally collected supervised data are available, and analytical models from domain expertise and existing unsupervised data sets are leveraged in addition to solve inverse problems in a semi-supervised fashion. This minimises the supervised data collection requirements and allows the training of effective probabilistic recovery models relatively inexpensively. This novel method is first evaluated in quantitative simulated experiments, testing performance in various controlled settings and compared to alternative techniques. The framework is then implemented in several real world applications, spanning imaging, astronomy and human-computer interaction. In each real world setting, the novel technique makes use of all available information for training, whether this is simulations, data or both, depending on the task. In each experimental scenario, state of the art recovery and uncertainty estimation were demonstrated with reasonably limited experimental collection efforts for training. The second framework presented in this thesis approaches instead the challenging unsupervised situation, where no examples of ground-truths are available. This type of inverse problem is commonly encountered in data pre-processing and information retrieval. A variational framework is designed to capture the solution space of inverse problem by using solely an estimate of the observation process and large ensembles of observations examples. The unsupervised framework is tested on data recovery tasks under the common setting of missing values and noise, demonstrating superior performance to existing variational methods for imputation and de-noising with different real data sets. Furthermore, higher classification accuracy after imputation are shown, proving the advantage of propagating uncertainty to downstream tasks with the new model.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Colleges/Schools: College of Science and Engineering > School of Computing Science
• Funder's Name: Engineering and Physical Sciences Research Council (EPSRC), Engineering and Physical Sciences Research Council (EPSRC), Engineering and Physical Sciences Research Council (EPSRC)
• Supervisor's Name: Murray-Smith, Prof. Roderick
• Date of Award: 2021
• Depositing User: Theses Team
• Unique ID: glathesis:2021-82994
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 17 Jun 2022 14:28
• Last Modified: 17 Jun 2022 14:28
• Thesis DOI: 10.5525/gla.thesis.82994
• URI: https://theses.gla.ac.uk/id/eprint/82994

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